Meaning of the part-whole relation and the concept of fraction for primary teachers

The part-whole relation is complex and raises questions that affect different disciplines. Researchers have proposed different interpretations of the notions of fraction and rational number (e.g., Behr, Lesh, Post & Silver, 1983; Kieren, 1976). We highlight three kinds of relations in the study of rational numbers—the part whole-relation, the part-part relation, and the functional relation—through which we organize the different subconstructs of rational number. We claim that the meaning of fractions should be understood through three components: their mathematical structure, their representations and their senses

Philosophy & Architecture

Philosophy & Architecture special number of philosophy@LISBON (International eJournal) 5 | 2016 edited by Tomás N. Castro with Maribel Mendes Sobreira Centro de Filosofia da Universidade de Lisboa ISSN 2182-437

CASTRO: A New Compressible Astrophysical Solver. II. Gray Radiation Hydrodynamics

We describe the development of a flux-limited gray radiation solver for the compressible astrophysics code, CASTRO. CASTRO uses an Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically-rectangular variable-sized grids with simultaneous refinement in both space and time. The gray radiation solver is based on a mixed-frame formulation of radiation hydrodynamics. In our approach, the system is split into two parts, one part that couples the radiation and fluid in a hyperbolic subsystem, and another parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem is solved explicitly with a high-order Godunov scheme, whereas the parabolic part is solved implicitly with a first-order backward Euler method.Comment: accepted for publication in ApJS, high-resolution version available at https://ccse.lbl.gov/Publications/wqzhang/castro2.pd

Artrópodes infestantes de plantas comercializadas em supermercados no Distrito Federal, Brasil

Many Brazilian supermarkets offer ornamental and fruit plants for sale, and many become infested by insects and other arthropods during commercialization. This work reflects the importance of knowing the pests that occur in these plants, to verify possible dissemination of these arthropods to other areas. This study was carried out with monthly visits to five supermarkets chosen at random in the Federal District, Brazil. The plants were identified and visually inspected for the presence of insects and other arthropods. The collected specimens were preserved in jars containing 70% alcohol. Their respective levels of infestation and damage were also observed and noted. Each specimen collected was identified according to specific books and keys for each taxonomic group collected. As a result, 65 plants were found to be infested with insects and mites. Of these, 48 contained sucking insects (Hemiptera) and 17 had spider mites (Tetranychus urticae Koch). Although the insects found are relatively common and have already been reported to be associated with several ornamental plants, this is the first work that records the occurrence of arthropods in ornamentals sold in commercial establishments.Os principais mercados brasileiros oferecem plantas ornamentais e frutíferas para a venda e muitas delas acabam sendo infestadas por insetos e outros artrópodes durante a comercialização. Esse trabalho reflete a importância de se conhecer as pragas que ocorrem nessas plantas, com o propósito de verificar um possível meio de disseminação desses animais para outras áreas. O presente trabalho foi realizado com visitas mensais em cinco supermercados escolhidos de forma aleatória situados no Distrito Federal, Brasil. As plantas foram identificadas e inspecionadas visualmente quanto à presença de insetos e outros artrópodes. Os espécimes coletados foram preservados em potes contendo álcool 70% e seus respectivos níveis de infestação e danos também foram observados e anotados. A identificação de cada exemplar coletado foi feita de acordo com livros e chaves específicas para cada grupo taxonômico encontrado. Como resultado, foram encontradas 65 plantas infestadas com insetos e ácaros. Destas, 48 continham insetos sugadores (Hemiptera) e 17 estavam com ácaro-rajado (Tetranychus urticae Koch). Apesar dos insetos encontrados serem relativamente comuns e já terem sido relatados associados a várias plantas ornamentais, esse é o primeiro trabalho que registra a ocorrência de artrópodes em ornamentais vendidas em estabelecimentos comerciais